Strong limit theorems for increments of sums of independent random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 7, Tome 311 (2004), pp. 260-285

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We derive universal strong laws for increments of sums of independent nonidentically distributed random variables. These results generalize universal results of the author for i.i.d. case which include the strong law of large numbers, the law of the iterated logarithm, the Erdős–Rényi law and the Csörgő–Révész laws.
@article{ZNSL_2004_311_a15,
     author = {A. N. Frolov},
     title = {Strong limit theorems for increments of sums of independent random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {260--285},
     publisher = {mathdoc},
     volume = {311},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a15/}
}
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A. N. Frolov. Strong limit theorems for increments of sums of independent random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 7, Tome 311 (2004), pp. 260-285. http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a15/